Systems and methods for blind mode adaptive equalization with multiple algorithms

ABSTRACT

Various embodiments described herein are directed to methods and systems for blind mode adaptive equalizer system to recover complex valued data symbols from the signal transmitted over time-varying dispersive diversity wireless channels. For example, various embodiments may utilize an architecture comprised of a bank of estimation units, a normalizing gain estimator, a DSP unit and a feedback shift register providing the equalizer feedback state vector. The estimation unit may be further comprised of a multiplicity of adaptive algorithms providing various filtered estimates of the data symbol to the DSP unit or providing the joint estimate of the transmitted data symbol.

BACKGROUND

Broadband wireless systems are currently in a rapid evolutionary phasein terms of development of various technologies, development of variousapplications, deployment of various services and generation of manyimportant standards in the field. The increasing demand on variousservices justifies the need for the transmission of data on variouscommunication channels at the highest possible data rates. The multipathand fading characteristics of the wireless channels result in variousdistortions, the most important of those being the inter-symbolinterference (ISI) especially at relatively high data rates. Adaptiveequalizers are employed to mitigate the ISI introduced by the timevarying dispersive channels and possibly arising from other sources. Inone class of adaptive equalizers, a training sequence known to thereceiver is transmitted that is used by adaptive equalizer for adjustingthe equalizer parameter vector to a value that results in a relativelysmall residual ISI. After the training sequence, the data is transmittedduring which period the equalizer continues to adapt to slow channelvariations using decision directed method.

Among the various algorithms to adapt the equalizer parameter vector arethe recursive least squares (RLS) algorithm, exponentially weightedKalman filter, LMS algorithm, and the quantized state (QS) algorithm,the last one taught by Kumar et. al. in, “Adaptive Equalization Via FastQuantized-State Methods”, IEEE Transactions on Communications, Vol.COM-29, No. 10, October 1981. Kumar at. al. teach orthogonalizationprocess to arrive at fast and computationally efficient identificationalgorithms in,” State Inverse and Decorrelated State StochasticApproximation”, Automatica, Vol. 16, May 1980. The training approach,however, is not desirable in many communication applications such asthose involving video conference type of applications that will requirea training sequence every time a different speaker talks. Moreover, theneed for training sequence results in a significant reduction incapacity as for example, in GSM standard, a very significant part ofeach frame is used for the equalizer training sequence. Also, if duringthe decision-directed mode the equalizer deviates significantly due toburst of noise or interference, all the subsequent data will beerroneously received by the receiver until the loss of equalization isdetected and the training sequence is retransmitted and so on.

There are many other applications where the equalizers are applied as inantenna beam forming, adaptive antenna focusing of the antenna, radioastronomy, navigation, etc. For example, Kumar et. al. teach in Methodand Apparatus for Reducing Multipath Signal Error Using Deconvolution,U.S. Pat. No. 5,918,161, June 1999, an equalizer approach for a verydifferent problem of precise elimination of the multipath error in therange measurement in GPS receiver. In all of various applications ofequalizers and due to various considerations such as the logistics andefficiency of systems, it has been of great interest to have theequalizer adapt without the need for a training sequence. Suchequalizers are the termed the blind mode equalizers.

Among some of the approaches to blind mode equalization is the Sato'salgorithm that is similar to the LMS algorithm except that it does nothave any training period. Kumar in, “Convergence of A Decision-DirectedAdaptive Equalizer,” Proceedings of the 22^(nd) IEEE Conference onDecision and Control, 1983, Vol. 22, teaches a technique wherein anintentional noise with relatively high variance is injected into thedecision-directed adaptive algorithm with the noise variance reduced asthe convergence progressed and shows that the domain of convergence ofthe blind mode equalizer was considerably increased with the increase inthe noise variance at the start of the algorithm. The technique taughtby Kumar is analogous to the annealing in the steel process industry andin fact the term simulated annealing was coined after the introductionby Kumar. Lambert et. al., teach the estimation of the channel impulseresponse from the detected data in, “Forward/Inverse BlindEqualization,” 1995 Conference Record of the 28^(th) Asilomar Conferenceon Signals, Systems and Computers, Vol. 2, 1995.

Another blind mode equalization method applicable to the case where themodulated data symbols have a constant envelope and known as Goddard orconstant modulus algorithm (CMA) is based on minimization of themagnitude square of the estimate of the estimate of the data symbol anda constant that may be selected to be 1. An example of references forthe CMA is W. Chung, et. al., “The local minima of fractionally-spacedCMA blind equalizer cost function in the presence of channel noise,”Proc. IEEE International Conference on Acoustics, Speech, and SignalProcessing, pp. 3345-8, 12-15 May, 1998.

Some of the prior blind mode equalizers have relatively long convergenceperiod and are not universally applicable in terms of the channels to beequalized and in some cases methods such as the one based on polyspectraanalysis are computationally very expensive. The CMA method is limitedto only constant envelope modulation schemes such as M-phase shiftkeying (MPSK) and thus are not applicable to modulation schemes such asM-quadrature amplitude modulation (MQAM) and M-amplitude shift keying(MASK) modulation that are extensively used in wireless communicationsystems due to their desirable characteristics. Tsuie et. al. in,Selective Slicing Equalizer, Pub. No. US 2008/0260017 A1, Oct. 23, 2008,taught a selective slicing equalizer wherein in a decision feedbackequalizer configuration, the input to the feedback path may be selectedeither from the combiner output or the output of the slicer dependingupon the combiner output. Kumar in, Systems and Methods for AdaptiveBlind Mode Equalization, U.S. patent application Ser. No. 13/434,498,Mar. 29, 2012, teaches blind mode equalizer with hierarchicalarchitecture.

The prior blind mode equalization techniques are for the case of asingle channel that may be the result of combining the signals receivedover multiple diversity channels before equalization. Such an approachdoes not take advantage of the differences that may exist among thediversity channels. Some of the algorithms have relatively slowconvergence rate and may be limited in terms of their applicability tovarious modulation formats. It is desirable to have blind mode adaptiveequalizers that are efficient for the case of the signal received overdispersive diversity channels, possess robustness and some level ofinherent redundancy to avoid convergence to any local minima, have wideapplicability without, for example, restriction of constant modulussignals, are relatively fast in convergence, are computationallyefficient, have modular configuration to provide a tradeoff betweencomplexity and performance. The equalizers of this invention possessthese and various other benefits.

SUMMARY OF THE INVENTION

Various embodiments described herein are directed to methods and systemsfor blind mode multiple algorithms adaptive equalizer system (BMMAES) torecover the in general complex valued data symbols from the signaltransmitted over time-varying dispersive wireless channels. For example,various embodiments may utilize an architecture comprised of anormalizing gain estimator, an estimation unit for providing amultiplicity N filtered estimates of the data symbols, and a DSP unitfor providing a jointly detected data symbol based on the multiplicity Nfiltered estimates. In the decision feedback configuration, thearchitecture is further comprised of a feedback shift register forproviding a feedback state vector, comprised of the delayed versions ofthe jointly detected data symbol, to the estimation unit for eliminatingthe inter symbol interference (ISI) due to the past symbols.

In the feed forward mode of the equalizer architecture, the estimationunit is further comprised of a feed forward shift register for providinga feed forward state vector to a first multiplicity N inner productoperators providing the N feed forward signals, on the basis of therespective equalizer forward weight vectors, for generating the N errorsignals for updating the multiplicity N adaptive algorithms that providethe N equalizer forward weight vectors.

In the decision feedback mode of the equalizer architecture, theestimation unit is further comprised of a second multiplicity N innerproduct operators providing the N feedback signals on the basis of therespective equalizer feedback weight vectors, for modifying the N errorsignals for updating the multiplicity N adaptive algorithms that providethe N equalizer weight vectors comprised of the respective feed forwardand feedback weight vectors.

The normalizing gain estimator is further comprised of a bank of Nparameter α estimators wherein the i^(th) parameter □ estimator providesthe estimate of the parameter α_(i) for normalizing the filteredestimate, on the basis of the i^(th) filtered estimate s_(i) of the datasymbol and the equalizer forward weight vector from the i^(th) adaptivealgorithm for i=1, 2, . . . , N. The parameter α estimator is furthercomprised of an estimator of the power in the filtered estimate, and anestimator of the power in the noise component of the filtered estimate,for obtaining the estimate of the power of the signal component of thefiltered estimate.

The DSP unit is further comprised of a bank of phase alignment subsystemunits for providing gain normalization and phase alignment of the Nfiltered signals, a reference phase generator for generating thereference phase, a means of further adjusting the phase of the filteredsignals, a combiner weights generator, a weighted combiner for weightedcombining of the phase adjusted signals, and a decision device forproviding the jointly detected data symbol.

The i^(th) phase alignment subsystem unit for i=1, 2, . . . , N, isfurther comprised of a gain normalizer for normalizing the power in thesignal component of the filtered estimate to the signal power in thedata symbols, a phase accumulator unit for providing the phase alignmentof the i^(th) filtered estimate, a decision device for providing thei^(th) detected data symbol based on the i^(th) filtered estimate, aphase threshold device for providing the detected phase φ_(i), and ameans for estimating the signal to residual inter symbol interference(ISI) plus noise power ratio Γ_(i) for the i^(th) filtered estimate.

The phase threshold device determines the sector in the signalconstellation diagram of the data symbol in which the phase alignedfiltered estimate lies, wherein the sector in the signal constellationdiagram may be one of the sectors of rotational symmetry in theconstellation diagram. For example, the data symbol may be a MQAMmodulated signal with the order of modulation M=N² for some integer N,and has four sectors of rotational symmetry. In various otherembodiments of the invention, the sectors may correspond to the fourquadrants of the constellation diagram for any signal constellationdiagram.

Various embodiments of the blind mode multiple algorithms equalizersystem (BMMAES) to recover the in general complex valued data symbolsfrom the signal transmitted over dispersive diversity wireless channelswith order of diversity N_(c) may utilize an architecture comprised of anormalizing gain estimator, a bank of N_(c) estimation units wherein theestimation unit is for receiving the signal over one of the N_(c)diversity channels and providing N_(a) filtered estimates on the basisof N_(a) adaptive algorithms, a collator for collating the filteredestimates of the data symbols from the bank of N_(c) estimation unitsproviding the collated N filtered estimates of the data symbols providedby the N_(c) estimation units, and a DSP unit for providing the jointlydetected data symbol based on the collated N filtered estimates of thedata symbols. In the feedback configuration, the architecture is furthercomprised of a feedback shift register for providing a feedback statevector, comprised of the delayed versions of the jointly detected datasymbol, to the N_(c) estimation units for eliminating the inter symbolinterference (ISI) due to the past symbols.

The various adaptive algorithms in the N_(c) estimation units may all bedistinct and, for example, may be selected from the group consisting ofthe recursive least squares (RLS) algorithm, various quantized state(QS) algorithms, LMS algorithm, Sato's algorithm, Goddard algorithm,neural based algorithm, the blind mode algorithm with hierarchicalstructure, or any other more general linear or nonlinear algorithm forobtaining the filtered estimates of the data symbols. In someembodiments, several versions of the same algorithm with differentalgorithm parameters, for example, the initial estimate of the equalizerweight vector, may be used in the estimation units.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the present invention are described here by wayof example in conjunction with the following figures, wherein

FIG. 1 shows a block diagram of one embodiment of blind mode adaptiveequalizer system with multiple algorithms.

FIG. 2 is shows a block diagram of one embodiment of normalizing gainestimator.

FIG. 2A shows a block diagram of one embodiment of parameter αestimator.

FIG. 3 shows a block diagram of one embodiment of DSP unit.

FIG. 4 shows a block diagram of one embodiment of phase alignmentsubsystem.

FIG. 5 shows the block diagram of one embodiment of equalizer system fordispersive diversity channels.

FIG. 6 shows one embodiment of an example computer device.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description is provided to enable any person skilled inthe art to make and use the invention and sets forth the best modescontemplated by the inventor of carrying out his invention. Variousmodifications, however, will remain readily apparent to those skilled inthe art, since the generic principles of the present invention have beendefined herein specifically to provide systems and methods for blindmode equalization of signals received over time varying dispersivechannels, and for recovering the data symbols transmitted from a sourcein blind mode.

FIG. 1 shows the block diagram of one of the various embodiments of theinvention. Referring to FIG. 1 the input 10 z(k+K₁) wherein k denotesthe discrete time with K₁ some constant integer, to the blind modeequalizer 1 is in general a complex valued signal that may be the outputof the discrete-time channel, not shown, with impulse response h(k) andthe input to the discrete-time channel given by the in general complexvalued data symbol sequence a(k). The channel impulse response may be aslowly varying function of time.

The data symbol a(k) may take values from a set of M possible values forsome integer M. For example, for the case of the QPSK modulation indigital communication systems, a_(k)=a_(I,k)+j a_(Q,k), with j=√{squareroot over (−1)}, and with a_(I,k) and a_(Q,k) denoting the real andimaginary components of a_(k) taking possible values+A₀ and −A₀ for someconstant A₀>0. For the case of MQAM modulation with the number of pointsM in the signal constellation equal to N² for some positive integer Nthat is normally selected to be an integer power of 2, each of a_(I,k)and a_(Q,k) may take possible values from the set of N values given by{±1, ±3, . . . , ±(N−1)}A₀. Similarly for the MPSK modulation, a_(k)takes possible values from the set of M values given by{A₀exp(j((2m−1)π/M);m=1, 2, . . . , M}.

The output z(k) of the discrete-time channel is given by

$\begin{matrix}{\begin{matrix}{{y_{c}(k)} = {\sum\limits_{i = {- M_{1}}}^{M_{1}}{{h(i)}{a\left( {k - 1} \right)}}}} \\{{= {{\overset{\_}{h}}^{H}{\overset{\_}{\chi}}_{k}}};}\end{matrix}{{\overset{\_}{\chi}}_{k} = \left\lbrack {{a\left( {k_{0} + M_{1}} \right)},\ldots \mspace{14mu},{a\left( k_{0} \right)},\ldots \mspace{14mu},{a\left( {k_{0} - M_{1}} \right)}} \right\rbrack^{T}}} & \left( {1a} \right) \\{{\overset{\_}{h}}^{T} = \left\lbrack {{h\left( {- M_{1}} \right)}\mspace{14mu} \ldots \mspace{14mu} {h\left( {- 1} \right)}{h(0)}{h(1)}\mspace{14mu} \ldots \mspace{14mu} {h\left( M_{1} \right)}} \right\rbrack} & \left( {1b} \right) \\{{{{z(k)} = {{y_{c}(k)} + {n(k)}}};}{{k = 0},1,\ldots}} & \left( {1c} \right)\end{matrix}$

wherein H denotes the conjugate transpose and T denotes the transposeoperations.

Referring to FIG. 1, the complex valued signal z(k+K₁) is inputted tothe estimation unit 95. The complex valued signal z(k+K₁) is inputted tothe feed forward shift register 20 of length K₁ providing the delayedversions 25 z(k+K₁−1), . . . , z(k) of the input z(k+K₁) to the scalarto vector converter 26 that provides the forward state vector 28x_(f)(k)=[z(k+K₁)z(k+K₁−1) . . . z(k)]^(T) at the output of the scalarto vector converter 26. Referring to FIG. 1, the forward state vectorx_(f)(k) is inputted to the N vector inner product operators 32 a, b, .. . , N. Throughout the description of the invention, the notations **a,b, . . . , N and **1, 2, . . . , N for any integer ** are equivalent andboth refer to the enumeration between 1 and N. The other inputs of the Nvector inner product operators 32 are provided with the N equalizerforward weight vectors 30 w_(1f)(k), w_(2f)(k), . . . , W_(Nf)(k).Referring to FIG. 1, the N equalizer forward weight vectors 30 a, b, . .. , N are provided by the N adaptive algorithm blocks 40 a, b, . . . , Nrespectively. Referring to FIG. 1, the outputs 41 a, b, . . . , Ny_(1f)(k), y_(2f)(k), . . . , y_(Nf)(k) are inputted to the adders 42 a,b, . . . , N respectively. The other inputs of the adders 42 a, b, . . ., N are provided with the feedback signals 39 y_(1b)(k), y_(2b)(k), . .. , y_(Nb)(k) respectively.

Referring to FIG. 1, the outputs 45 a, b, . . . , N s₁(k), s₂(k), . . ., s_(N)(k) of the adders 42 denoting the N filtered estimates of thediscrete-time channel input symbol a(k) are inputted to the DSP unitblock 60. The DSP unit 60 is also inputted with the ac parameters 185 a,b, . . . , N α₁(k), α₂(k), . . . , α_(N)(k) made available from thenormalizer gain estimator 90. The DSP unit processes the N filteredestimates 45 of the symbol a(k) and the N a parameter estimates 185 andprovides the joint estimate 65 â(k) of the symbol at the output of theDSP unit. Referring to FIG. 1, the normalizer gain estimator 90 isinputted with the equalizer forward weight vectors 30 a, b, . . . , Nprovided by the adaptive algorithm blocks 40 a, b, . . . , N.

Referring to FIG. 1, the joint estimate 65 â(k) is inputted to thefeedback shift register 70 that provides the K₂ delayed versions 75 ofthe joint estimate â(k) given by â(k−1), â(k−2), . . . , â(k−K₂) at theoutput of the feedback shift register. The delayed versions 75 â(k−1),â(k−2), . . . , â(k−K₂) are inputted to the scalar to vector converter76 that provides the feedback state vector x_(b)(k)=[â(k−1)â(k−2) . . .â(k−K₁)]^(T) to the N vector inner product operators 38 a, b, . . . , N.The other inputs of the N vector inner product operators 38 are providedwith the N equalizer feedback weight vectors 35 w_(1b)(k), w_(2b)(k), .. . , w_(Nb)(k). Referring to FIG. 1, the N equalizer feedback weightvectors 35 a, b, . . . , N are provided by the N adaptive algorithmblocks 40 a, b, . . . , N respectively.

In some embodiments of the invention, none of the N equalizer adaptivealgorithms may be of the decision feedback type and thus K₂ is set equalto zero. In such embodiments, the feed forward shift register 20 is oflength (K₁+K₂) providing the delayed versions 25 z(k+K₁−1), . . . ,z(k), . . . , z(k−K₂) of the input z(k+K₁) to the scalar to vectorconverter 26.

Referring to FIG. 1, the outputs 39 a, b, . . . , N y_(1b)(k),y_(2b)(k), . . . , y_(Nb)(k) are inputted to the adders 42 a, b, . . . ,N respectively. The signals 39 a, b, . . . , N y_(1b)(k), y_(2b)(k), . .. , y_(Nb)(k) are to compensate for any inter symbol interferencecontribution due to the past symbols wherein the y_(1f)(k), y_(2f)(k), .. . , y_(Nf)(k) inputs to the adders 42 compensate for the inter symbolinterference contribution due to the future symbols.

Referring to FIG. 1, the N filtered estimates of the symbol a(k) givenby s₁(k), s₂(k), . . . , s_(N)(k) at the outputs of the adders 42 areinputted to the adders 55 a, b, . . . , N respectively. The other inputsof the adders 55 a, b, . . . , N are provided with the joint estimate ofthe symbol â(k). The adders 55 a, b, . . . , N compare the filteredestimates s₁(k), s₂(k), . . . , s_(N)(k) with the joint estimate of thesymbol â(k) providing the error signals e₁(k), e₂(k), . . . , e_(N)(k)to the N adaptive algorithm blocks 40 a, b, . . . , N respectively. Theadaptive algorithms adjust their estimates of the equalizer forward andfeedback weight vectors so as to adaptively minimize some appropriatemeasures of the error signals e₁(k), e₂(k), . . . , e_(N)(k), such asthe mean squared error, wherein different adaptive algorithm may usedifferent such measures. Referring to FIG. 1, the N adaptive algorithmblocks 40 a, b, . . . , N are inputted with the feed forward statevector x^(f)(k) and the feedback state vector x^(b)(k) for theadaptation of the equalizer weight vectors.

Referring to FIG. 1, the N adaptive algorithms 40 a, b, . . . , N invarious embodiments of the invention, may be selected from the variouslinear or nonlinear adaptive algorithms such as the LMS algorithm, therecursive least squares (RLS) algorithm, or the quantizes statealgorithm with â(k) as the reference input, may be one of the blind modealgorithms such as the Sato or the Goddard algorithm or any other linearor nonlinear adaptive algorithm such as the one based on the neuralnetworks. In various embodiments of the invention, some of the Nadaptive algorithms may be same but with different algorithm parametersand possibly with different initial estimates for the equalizer weightvectors. Use of different adaptive algorithms in obtaining the jointestimate of the symbol a(k) may result in inheriting distinct advantagesof the various adaptive algorithms, for example, some of the algorithmshave faster convergence speed while the others may be more robustagainst modeling inaccuracies while some may be advantageous in terms ofpossibility of diverging to some spurious weight vectors.

Taking into account the gain introduced by the parameter α(k), the LMSadaptive algorithm is given by

w _(iu)(k+1)=w _(iu)(k)+μ(k)x(k)({circumflex over (a)}(k)−s _(i)(k))*;s_(i)(k)=w _(iu) ^(H)(k);k=0,1, . . .   (2a)

w _(i)(k+1)=α_(i) ⁻¹(k)w _(iu)(k+1)  (2b)

In (2a, b) â(k) is the joint symbol estimate provided by the DSP unit60, μ(k) may be an appropriately selected sufficiently small positivescalar constant to achieve convergence or may be a decreasing positivefunction of k, * denotes complex conjugate operation and the equalizerstate vector x(k) and the equalizer weight vector w_(i)(k) of dimensionK=(K₁+K₂+1) given by

x(k)=[x _(f) ^(H)(k)x _(b) ^(H)(k)]^(H) ;w _(i)(k)=[w _(if) ^(H)(k)w_(ib) ^(H)(k)]^(H)  (3)

In (3) H denotes the Hermitian transpose and in (2) the initial estimatefor the vector w_(iu)(k) at k=0 may be selected equal to [0 0 . . . 0 10 . . . 0]^(H) with the only nonzero element in the (K₁+1)^(st) positionequal to 1 and with α_(i)(0) selected equal to 1.

In various embodiments of the invention, one or more of the adaptivealgorithms 40 may be the RLS algorithm given by

{circumflex over (w)} _(iu)(k+1)= {circumflex over (w)} _(iu)(k)+μ(k)R_(k) x _(k)({circumflex over (a)}(k)−s _(i)(k))*;s _(i)(k)=w _(iu) ^(H)x(k);  (4a)

R(k)=λ⁻¹ [R(k−1)−R(k−1) x _(k)( x _(k) ^(H) R(k−1) x _(k)+λ)⁻¹ x _(k)^(H) R(k−1)];k=1,2, . . .   (4b)

w _(i)(k+1)=α_(i) ⁻¹(k)w _(iu)(k+1)  (4c)

In (4b) â(k) is the joint symbol estimate provided by the DSP unit 60, λwith 0≦λ≦1 is the exponential weighting coefficient that determines theeffective averaging period in the evaluation of R(k) that may beinitialized at time k=0 by a diagonal matrix ε_(R)I_(K) for some smallpositive scalar ε_(R) with I_(K) denoting the (K×K) identity matrix. Useof the RLS algorithm as one of the N algorithms 40 in the system of FIG.1 may result in a faster convergence of the multiple algorithm blindmode equalizer. In various embodiments of the invention that involve useof the RLS algorithms in more than one of the algorithm blocks 40 a, b,. . . , N, the different versions of the RLS algorithm may havedifferent initial conditions for w_(u)(k) at k=0 and possibly usedifferent values of λ.

In various other embodiments of the invention one of the adaptivealgorithms 40 may be one of the quantized state algorithms such as theQS1 algorithm given by

$\begin{matrix}{{{{w_{iu}\left( {k + 1} \right)} = {{w_{iu}(k)} + {{\mu (k)}{{P_{I}^{q}(k)}\left\lbrack {{x^{q}(k)} + {\frac{{x^{qH}(k)}{x(k)}}{{x^{q}(k)}{x(k)}}{x(k)}}} \right\rbrack} \times \left( {{a(k)} - {s_{i}(k)}} \right)^{*}}}};}\mspace{79mu} {{s_{i}(k)} = {w_{iu}^{H}{x(k)}}}} & \left( {5a} \right) \\{{P^{q}(k)} = {{\lambda \; {P^{q}\left( {k - 1} \right)}} + {\left( {1 - \lambda} \right){x^{q}(k)}{x^{H}(k)}} + {\left( {1 - \lambda} \right){x(k)}{x^{qH}(k)}} + {\left( {1 - \lambda} \right)ɛ\; I}}} & \left( {5b} \right) \\{\mspace{79mu} {{{{w_{i}\left( {k + 1} \right)} = {{\alpha_{i}^{- 1}(k)}{w_{iu}\left( {k + 1} \right)}}};}\mspace{79mu} {{P_{I}^{q}(k)} = \left\lbrack {P^{q}(k)} \right\rbrack^{- 1}}}} & \left( {5c} \right)\end{matrix}$

In (5b, c) the matrix P_(I) ^(q)(k) may be updated directly withoutrequiring the matrix inversion with the application of the matrixinversion lemma to the update in (5b) and P_(I) ^(q)(k) at k=0 may beinitialized by a diagonal matrix ε_(P)I_(K) for some small positivescalar ε_(P) with I_(K) denoting the (K×K) identity matrix. In (5) thevector x^(q)(k) is obtained by replacing both the real and imaginarycomponents of the various elements of the vector x(k) with theirquantized versions. The i^(th) component of x^(q)(k) is given by (6).

x _(i) ^(q)(k)=_(gT)(Re(x _(i)(k)))+jg _(T)(Im(x _(i)(k)));j=√{squareroot over (−1)};i=1,2, . . . ,K  (6)

In (6) g_(T)(x) for x real is the threshold function defined in (7), andRe(z) and Im(z) denote the real and imaginary components of z for anycomplex variable z.

$\begin{matrix}{{g_{T}(x)} = \left\{ \begin{matrix}{{+ 1};{x > v_{th}}} \\{{- 1};{x < {- v_{th}}}} \\{0;{{x} < v_{th}}}\end{matrix} \right.} & (7)\end{matrix}$

In (7) v_(th) is some positive threshold value that may be set equal to0 in which case the function g_(T)(x) reduces to the signum function.The function g_(T)(x) may be modified such that for |x|<c_(th), thefunction g_(T)(X) is equal to ε sgn(x) for some small positive scalar εand with the signum function sgn(x) given by (10).

In various embodiments of the invention one of the adaptive algorithms40 may be the Sato's algorithm given by

w _(iu)(k+1)=w _(iu)(k)+μ(k)x(k)[γ₁ sgn(s _(i)(k))−s _(i)(k)]*;s_(i)(k)=w _(iu) ^(H) x(k);k=0,1, . . .   (8a)

w _(i)(k+1)=α_(i) ⁻¹(k)w _(iu)(k+1)  (8b)

In (8a) γ₁ is given by

γ₁ [|a(k)|² ]{E[|a(k)|]}⁻¹  (8c)

and sgn(s_(i)(k)) in (8a) is obtained by replacing both the real andimaginary components of s_(i)(k) with 1 bit quantized versions with

sgn(s _(i))=sgn(Re(s _(i)))+jsgn(Im(s _(i)));j=√{square root over(−1)}  (9)

In (9) Re(z) and Im(z) denote the real and imaginary components of z forany complex variable z and sgn(x) for x real is the signum functiondefined in (10).

$\begin{matrix}{{{sgn}(x)} = \left\{ \begin{matrix}{{+ 1};{x > 0}} \\{{- 1};{x \leq 0}}\end{matrix} \right.} & (10)\end{matrix}$

For the specific case of BPSK modulation wherein a(k) takes values +1and −1 with probability 0.5, γ in (8c) is equal to 1 and the Sato'salgorithm is same as the LMS algorithm in the decision directed mode.

In the various embodiments of the invention one of the adaptivealgorithms 40 may be the Godard's algorithm given by

w _(iu)(k+1)=w _(iu)(k)+μ(k)x(k)s _(i)*(k)|s _(i)(k)|^(p-2)[γ_(p) −|s_(i)(k)|^(p)];  (11a)

w _(i)(k+1)=α_(i) ⁻¹(k)w _(iu)(k+1);s _(i)(k)=w _(iu) ^(H) x(k);γ_(p)=E[|a(k)|^(2p) ]{E[|a(k)|^(p)]}⁻¹  (11b)

In (11) p is any positive integer wherein for the case of p=2 thealgorithm in (11a) reduces to

w _(iu)(k+1)=w _(iu)(k)+μ(k)x(k)s _(i)*(k)[γ_(p) −|s _(i)(k)|²];  (12)

In case of Sato's and Goddard's algorithms in (8)-(12), the correctionterm in the weight update algorithm depends directly upon the filteredsignal s_(i)(k) instead of the error term e_(i)(k)=(â(k)−s_(i)(k)). Insuch cases the estimation unit 95 in FIG. 95 may be modified by feedingback the signal 45 i s_(i)(k) to the adaptive algorithm 40 i.

In some of the various embodiments of the invention one of the adaptivealgorithms 40 may be a nonlinear algorithm wherein the estimate of thesymbol s_(i)(k) is a nonlinear function of the state vector x(k) insteadof the linear function given in the algorithms described by (4)-(12).For example, the estimate of the symbol s_(i)(k) may be obtained byneural network based implementation. For example, a superfast neuralnetwork based algorithm is taught in, “Superfast and Efficient ChannelEqualizer Architecture Based on Neural Network,” IEEE InternationalConference on Aerospace Engineering, Big Sky, Mont., March 2012, pp.1-11, that is included in its entirety as part of this application.While the neural network based algorithm is very fast in convergence, itrequires a training sequence. With one of the N algorithms 40 in FIG. 1selected to be the neural network based algorithm with another one, forexample, based on Sato's algorithm an overall very fast convergence maybe achieved in the blind mode.

FIG. 2 shows the block diagram of the normalizing gain estimator 90.Referring to FIG. 2, the normalizing gain estimator is comprised of abank of N parameter α estimation units 100 a through N. Referring toFIG. 2, the parameter α estimation units 100 i receives the equalizerfeed forward weight vector 30 i w_(if)(k) and the filtered estimate 45 is_(i)(k) form the estimation unit 95 of FIG. 1 and provides theparameter α_(i) estimate 185 i to the DSP unit 60 of FIG. 1 for i=1, 2,. . . , N.

FIG. 2A shows the block diagram of the unit 100 i parameter α_(ι)estimator for estimating the parameter α_(i). Referring to FIG. 2A, theequalizer feed forward weight vector 30 i w_(if)(k) is inputted to thenorm square block 105 that provides the norm square 110∥w_(if)(k)∥² tothe input of the multiplier 120. The other input of the multiplier 120is provided with the variance σ_(n) ², or an appropriate estimate ofσ_(n) ², of the noise n(k) at the discrete-time channel output. Theoutput 125 P_(n,i) of the multiplier 120 is an estimate of the noisepower present in the i^(th) equalizer output 45 i s_(i)(k).

Referring to FIG. 2A, the i^(th) equalizer output 45 i s_(i)(k) isinputted to the power estimator block 140 that provides the estimate ofthe total power P_(T,i)(k) in the signal s_(i)(k) at the output 145. Thepower estimate block 140 may estimate the power P_(T,i)(k) according to(13).

P _(c,i)(j)=λ_(p) P _(c,i)(j−1)+|s _(i)(j)|² ;j=1,2, . . .   (13a)

P _(T,i)(k)=P _(c,i)(k)(1−λ_(p))/(1−λ_(p) ^(k))  (13b)

In (13), λ_(p) with 0<λ_(p)<1 is the exponential weighting coefficientthat determines the effective averaging period in the evaluation of thepower P_(T,i)(k) wherein the initial value of P_(T,i)(0) may be setequal to 0.

Referring to FIG. 2A, the i^(th) equalizer output noise power P_(n,i) issubtracted from the total power estimate P_(T,i)(k) by the adder 150providing the signal power estimate 160 P_(u,i) to the input of thedivider 165. The other input 170 of the divider 165 is provided with theaverage power P_(s) of the symbol a_(k) at the discrete-time channeloutput with P_(S)=E[|a_(k)|²] wherein E denotes the expected valueoperator. The divider block 165 divides the power P_(s) by the estimateof the signal power P_(u,i) at the i^(th) equalizer output and providesthe result 175 (P_(s)/P_(u,i)) to the square root block 180. The squareroot block provides the estimate of the parameter α_(i) at the output185 i. The parameter α_(I) is used by the DSP unit 60 to scale thesignal s_(i)(k) such that the signal power at the output of the i^(th)equalizer is close to P_(S)=E[|a_(k)|²] as would be the case when theequalizer has converged and thus speeds up the convergence of the multialgorithm equalizer of FIG. 1. In some embodiments of the invention, theparameter α_(i) may not be updated after an initial convergence period.

FIG. 3 shows the block diagram of the DSP unit 60. Referring to FIG. 3,the parameter 185 a α ₁(k) and the filtered symbol estimate 45 a s₁(k)provided by the first equalizer are inputted to the phase alignmentsubsystem unit 210 a PAS1. The phase alignment subsystem unit 210 a PAS1normalizes the signal power present in the input s_(i)(k) to P_(s) withthe gain α₁(k) and aligns the phase of the signal s₁(k) with thefiltered symbol estimates 45 b, . . . , N s₂(k), . . . s_(N)(k) providedby the equalizers 2 through N and provides the gain normalized and phasealigned signal s_(p,1)(k) at the output 215 a. In a likewise manner thephase alignment subsystem units 210 b through N PAS 2, . . . , PAS Nnormalize the signal power present in the inputs s₂(k), . . . , s_(N)(k)to P_(s) with the gains α₂(k), . . . , α_(N)(k), and align the phase ofthe signals s₂(k), . . . , s_(N)(k) with s₁(k) and with each otherproviding the gain normalized and phase aligned signal S_(p,2)(k), . . ., s_(p,N)(k) at the outputs 215 a through N.

FIG. 4 shows the block diagram of the phase alignment subsystem unit 210i for i=1, 2, . . . , N. Referring to FIG. 4, the filtered symbolestimate 45 i s_(i)(k) provided by the i^(th) equalizer comprised of theadaptive algorithm block 40 i, is inputted to the multiplier 305. Theother input of the multiplier 305 is inputted with the parameter 185 i α_(i)(k). The multiplier 305 provides the gain normalized signal 308s_(g,i)=α_(i)(k) s_(i)(k) to the multiplier 310. Referring to FIG. 4,the other input of the multiplier 310 is connected to the output of theexponential function block 340 that provides the output 342 exp[jφ_(c,i)(k−1)], j=√{square root over (−1)}, to the multiplier 310wherein φ_(c,i)(k−1) is the requisite phase rotation performed on thesignal s_(i)(k) for the purpose of the phase alignment. Referring toFIG. 4, the gain normalized and phase aligned signal 215 s_(p,i) isinputted to the decision device 350 that provides the detected signal355 â_(i)(k) at the output of the decision circuit computed according tothe decision function Δ( ).

The selection of the decision function Δ( ) depends upon the probabilitydistribution of the data symbols a_(k)=a_(I,k)+j a_(Q,k), withj=√{square root over (−1)}, and with a_(I,k) and a_(Q,k) denoting thereal and imaginary components of a_(k). For example, for the case of thediscrete type of the probability distribution of the data symbols a_(k)with both the real and imaginary components a_(I,k) and a_(Q,k) of a_(k)taking possible values from the finite sets Σ_(I) and Σ_(Q) respectivelyand where the components a_(I,k) and a_(Q,k) are statisticallyindependent as is the case, for example, for the MQAM modulated signals,the decision function may be given by (14).

D(â _(I,k) +Jâ _(Q,k))=D _(I)(â _(I,k))+jD _(Q)(â _(Q,k))  (14)

In (14) the functions Δ_(I)( ) and Δ_(Q)( ) may be the slicer functions.For the specific case when both the sets Σ_(I) and Σ_(Q) are equal tothe set {±1,±3, . . . , ±(N−1)}A₀ for some positive constant A₀ and someinteger N, the two slicer functions Δ_(I)(x) and Δ_(Q)(x) with x real,are identical and are given by (15).

D _(I)(x)=D _(I)(x)=D _(m)(|x|)sgn(x)  (15)

In (15), sgn(x) is the signum function given by (10) and the functionD_(m)(|x|) is given by

D _(m)(|x|)=iA ₀ ;V _(t) _(i−1) ≦|x|<V _(t) _(i) ;i=1,2, . . .,N/2  (16)

In (16), V_(t) _(i) for i=0, 1, . . . , N/2 are the threshold levelsgiven by

$\begin{matrix}{V_{t_{i}} = \left\{ \begin{matrix}{0;{i = 0}} \\{{2{iA}_{0}};{0 < i < {N/2}}} \\{\infty;{i = {N/2}}}\end{matrix} \right.} & (17)\end{matrix}$

The decision function described by (14)-(17), for example, applies tothe case where a_(k) is obtained as a result of MQAM modulation, withthe number of points in the signal constellation M=N². For othermodulation schemes and different probability distributions of the datasymbol, other appropriate decision functions may be employed. For thespecific case of M=4 corresponding to the QPSK modulation, the decisionfunction in (20) reduces to

D(â _(I,k) +jâ _(Q,k))=sgn(â _(I,k))+jsgn(â _(Q,k))  (18)

For the case of MPSK modulation with M>4, the decision device maycomprise of a normalizer that normalizes the complex data symbol by itsmagnitude with the normalized data symbol operated by the decisionfunction in (14)-(15).

Referring to FIG. 4, the detected symbol 355 â_(i)(k) is inputted to theblock 365 that evaluates the phase 382 θ_(i)(k) of the detected symbolâ_(i)(k). The phase 382 θ_(i)(k) is inputted to the phase thresholddevice 385 that provides the output 220 φ_(i)(k) according to thedecision function Δ_(p)( ) given by (19).

φ_(i)(k)=D _(p)(θ_(i)(k))=θ_(r,j);θ_(t) _(j) ≦θ_(i)(k)<θ_(t) _(j+1);j=0,1, . . . ,S−1  (19)

In (19) N_(s) denotes the order of symmetry of the signal constellationdiagram of the symbol â(k) equal to the number of distinct phaserotations of the signal constellation diagram that leave the signalconstellation unchanged and is equal to the number of phase ambiguitiesthat may be introduced by the blind mode equalizer. In (19) θ_(t) _(j) ;j=0, 1, . . . , N_(s) are the N_(s) threshold levels of the phasethreshold device 385.

As an example of the threshold values in (19), the signal constellationdiagram of the MQAM signal with a square grid constellation with thenumber of points in the signal constellation M equal to N² for someinteger N, has order of symmetry N_(s) equal to 4 with the possiblephase ambiguities equal to 0, π/2, π, 3π/2 as the rotation of the signalconstellation diagram by any of the four values 0, π/2, π, 3π/2 leavesthe signal constellation unchanged. The threshold levels for the MQAMsignal are given by θ_(t)0=0, θ_(t)1=π/2, θ_(t)2=π, θ_(t)3=3π/2. Therange of the phase given by θ_(t) _(j) ≦θ_(i)(k)<θ_(t) _(j+1) definesthe i^(th) sector of the signal constellation diagram equal to thei^(th) quadrant of the signal constellation diagram for i=0, 1, 2, 3.The output of the phase threshold device 385 is equal to one of thephase values θ_(r,0)=π/4, π_(r,1)=3π/4, θ_(r,2)=5π/4, and θ_(r,3)=7π/4depending upon the sector in which the input phase θ_(i)(k) lies.

For the case of MPSK signal, wherein a_(k) takes possible valuesA₀exp[j(m+0.5)2π/M], j=√{square root over (−1)}; m=0, 1, . . . , (M−1)for some integer M that is normally taken equal to an integer power of2. For the case of MPSK modulation, order of symmetry N_(s) equal to Mwith the possible phase ambiguities equal to 0, 2π/M, π, 4π/M, . . . .[2(M−1)π/M] resulting in M sectors with the m^(th) sector defined interms of the phase θ by the interval 2πm/M≦θ<2π(m+1)/M, m=0, 1, . . . ,M−1. In various alternative embodiments of the invention, the number ofsectors may be selected equal to 4 corresponding to the four quadrantsof the signal space for any signal constellation. For the case of realsymbols a(k) and real channel impulse response h(k), the number ofsectors may be just equal to 2 corresponding to the sign of the signal308 s_(g,i) and phase rotation is replaced by a sign inversion.

As the different adaptive algorithms 40 may converge with any of the Spossible phase ambiguities, to achieve coherence among the N differentalgorithms and thereby speed up the convergence, the phase of thefiltered signals s₁(k), . . . , s_(N)(k) are aligned to a common phasereference. The phase alignment may be achieved by first determining areference φ_(r)(k) among the N phase outputs φ_(i)(k), i=0, 1, . . . , Nand then aligning all the phase of s_(i)(k), i=0, 1, . . . , N byadjusting the phase of s_(i)(k) by the differenceφ_(d,i)(k)=(φ_(r)(k)−φ_(i)(k)). The phase reference φ_(r)(k), forexample, may be selected on the basis of the estimate of the signal tointerference plus noise power ratio in the detected signal â_(i)(k).

Referring to FIG. 4, the gain normalized and phase aligned signal 215s_(p,i) is inputted to the power estimator 344 that provides theestimate of the total power 346 P_(i) present in the signal s_(p,i) tothe input of the divider 360. The power P_(i) may be estimated accordingto (13) with s_(i) replaced by s_(i,p). Referring to FIG. 4, the signals215 s_(p,i) and the detected symbol â_(i)(k) are inputted to the adder352 that provides the difference 357 equal toã_(i)(k)=(s_(p,i)(k)−â_(i)(k)) to the power estimator 370.

After the convergence of the i^(th) equalizer the detected symbolâ_(i)(k) is equal to the correct symbol with a possible phase ambiguityand is the equalization error ã_(i)(k) comprised of the residual noiseand intersymbol interference. Referring to FIG. 4, the equalizationerror ã_(i)(k) is inputted to the power estimator 370 that provides theestimate of the residual noise and intersymbol interference powerP_(I,i) to the divider 360. Referring to FIG. 4, the power estimate 380P_(I,i) is inputted to the adder 348. The adder 348 provides theestimate of the signal power 348 P_(d,i)=(P_(i)−P_(I,i)) to the divider360. Referring to FIG. 4, the divider 360 divides the estimate of thesignal power P_(d,i) by the estimate of the residual noise and intersymbol interference power P_(I,i) providing the signal to residual noiseplus interference power ratio 225 Γ_(i)(k)=(P_(d,i)/P_(I,i)) at theoutput of the divider 360.

Referring to FIG. 3, the N phase outputs φ₁(k), φ₂(k), . . . , φ_(N)(k)at the outputs of the phase alignment subsystems 210 1, . . . , N areinputted to the reference phase generator 250. The reference phasegenerator 250 partitions the phase outputs φ₁(k), φ₂(k), . . . ,φ_(N)(k) into a number of N_(p) sets such that the phase of all theterms in any one of the partitions are equal and equal to one of thereference phase. For example, for the case of MQAM signal with squaregrid constellation S is equal to 4 and the reference phase are equal toθ_(r,0)=π/4, θ_(r,1)=3π/4, θ_(r,2)=5π/4, and θ_(r,3)=7π/4. Referring toFIG. 3, the set S_(p) of the indices of the terms in the partition withthe maximum number of phase terms, wherein the indices take values inthe range of 1 to N, and the number of terms m_(p) in S_(p) is inputtedto the combiner weights generator block 260. For the case wherein, morethan one partitions have the number of terms equal to the maximum valuem_(p), the partition containing the term with the highest SNR Γ_(i) isselected to break the tie. Referring to FIG. 3, the SNR Γ_(i) is madeavailable to the reference phase generator 250 by the phase alignmentsubsystem 210 i for i equal to a through N, not shown in the Figure.Referring to FIG. 3, the reference phase is set equal to the value ofthe phase φ_(i)(k), i=1, 2, . . . , N in the partition thus selected.

Referring to FIG. 3, the reference phase φ_(r)(k) generated by thereference phase generator 250 is inputted to the adders 228 a, b, . . ., N. Referring to FIG. 3, the phase φ_(i)(k) at the output 220 i of thephase alignment subsystem 210 i is inputted to the adder 228 i for iequal to a through N. The adder 228 i subtracts the phase φ_(i)(k) fromthe reference phase and feeds back the difference 230 i φ _(d,i)(k) tothe input of the phase alignment subsystem 210 i.

Referring to FIG. 4, the difference phase 230 i φ _(d,i)(k) isaccumulated by the accumulator comprised of the adder 332 and the delay335 providing the accumulated phase 334 φ_(c,i)(k). The delayed version338 φ_(c,i)(k−1) of the phase 334 φ_(c,i)(k) is inputted to the complexexponential operation block 340. Referring to FIG. 4, the output 342 ofthe complex exponential operation block 340 given by exp[jφ_(c,i)(k−1)], j=√{square root over (−1)} is inputted to themultiplier 310 that introduces a phase rotation of φ_(c,i)(k−1) in thephase of the other input 308 s_(g,i)(k) of the multiplier 310. Referringto FIG. 4, the phase aligned signal 215 s_(p,i) is made available to thedecision device 350.

Referring to FIG. 3, the difference phase 230 i the difference phase 230i φ _(d,i)(k) is inputted to the exponential function block 235 i thatprovides the output exp[jφ_(d,i)(k)], j=√{square root over (−1)} to themultiplier 240 i for i equal to 1 through N. Referring to FIG. 3, theother input of the multiplier 240 i is connected to the gain normalizedand phase aligned signal s_(p,i) output 215 i made available by thephase alignment subsystem 210 i. Referring to FIG. 3, the multiplier 240i adjusts the phase of the signal s_(p,i) by the difference phase 230 iφ _(d,i)(k) and provides the phase adjusted signal s_(c,i) at the output242 i to the input of the multiplier 270 i for i equal to 1 through N.

Referring to FIG. 3, the outputs of the multipliers 270 i, i=1, 2, . . ., N are inputted to the adder 290. The adder 290 provides the weightedsum s(k) of the phase adjusted signals s_(c,1), . . . , S_(c,N) at theoutput 292. The multipliers 270 i, i=1, 2, . . . , N and the adder 290constitute the weighted combiner for the phase adjusted signalss_(c,i)(k).

Referring to FIG. 3, the SNR Fi is made available to the combiner weightgenerator 260 by the phase alignment subsystem 210 i, for i equal to athrough N. On the basis of the SNRs Γ_(i), i equal to a through N, andthe set S, and the number of elements m_(p) in the set S_(p) madeavailable by the reference phase generator 250, the combiner weightgenerator 260 generates the weights ψ₁, ψ₂, . . . , ψ_(N) that may be ingeneral complex valued. The complex conjugates of the combiner weightsψ₂, . . . , ψ_(N) are made available to the multipliers 270 i, i=1, 2, .. . , N by the combiner weight generator 260.

In various embodiments of the invention, the combiner weights may bebased on the maximal ratio combining technique wherein the combinerweights are given by (20).

$\begin{matrix}{{{\psi_{i} = {\Gamma_{i}/\Gamma}};}{{\Gamma = {\sum\limits_{i = 1}^{N}\Gamma_{i}}};}{{i = 1},2,\ldots \mspace{14mu},N}} & (20)\end{matrix}$

In various embodiments of the invention, all of the weights ψ_(i) may beset equal to 1/N corresponding to the equal gain diversity combiningtechnique. In yet other embodiments of the invention, the weightcorresponding to the highest SNR Fi may be set equal to 1 with all ofthe other (N−1) weights set equal to 0 corresponding to the switcheddiversity combining technique.

In some of the embodiments of the invention, nonzero weights may beassigned only to the signals with their indices in the set S_(p) withthe signals with their indices not in the set S_(p) assigned zeroweights. The weights with their indices within the set S, may be givenby (21).

$\begin{matrix}{{{\psi_{i} = {\Gamma_{i}/\Gamma_{s}}};}{\Gamma_{s} = {\sum\limits_{i \in S_{p}}^{\;}\Gamma_{i}}}{for}{{i \in S_{p}};}{\psi_{i} = 0}{for}{i \notin {Sp}}} & (21)\end{matrix}$

In alternative embodiments of the invention, all of the weights withtheir indices in the set S_(p) may be set equal to 1/m_(p) wherein m_(p)is the number of indices in the set S_(p), with the weights with theirindices not in the set S_(p) assigned the value 0. In yet otherembodiments of the invention, the weight with its index in the set S_(p)corresponding to the highest SNR may be set equal to 1 with all of the(N−1) weights set equal to 0.

In various other embodiments of the invention, the combiner weights maybe based on one of the adaptive algorithm selected from the set of RLS,LMS, QS, Sato's and Goddard's algorithms. For example, using the Sato'salgorithm the combiner weight vector ψ=[ψ₁ψ₂ . . . ψ_(N)]^(T) may beupdated by (22).

ψ(k+1)=ψ(k)+μ(k)ξ(k)[γ₁ sgn(g(k))−g(k)]*;g(k)=ψ^(H)(k)ξ(k)  (22a)

ξ(k)=[s _(c,1)(k)s _(c,2)(k) . . . s _(c,N)(k)]^(T) ;k=0,1, . . .  (22b)

γ₁ =E[|a(k)|² ]{E[|a(k)|]}⁻¹  (22c)

In (22a) μ(k) may be an appropriately selected sufficiently smallpositive scalar constant to achieve convergence or may be a decreasingpositive function of k.

In various embodiments of the invention, the data symbols a(k) aretransmitted over N_(c) diversity channels with impulse responsesh^(i)(k), i=1, 2, . . . , N_(c) and the receiver jointly detects thedata symbol a(k) on the basis of the N_(c) signals received over theN_(c) diversity channels. The impulse responses may be slowly varyingfunctions of time to which the receiver adapts. In addition to thewireless communication, such situations arise in many other fields, forexample, in Radar systems.

FIG. 5 shows the block diagram of one of the embodiments of theinvention wherein the signal is received over dispersive diversitywireless channel with order of diversity N_(c). Referring to FIG. 5, thesignals received over the diversity channels 510 a, b, . . . , N_(c)z¹(k+K₁), z²(k+K₁), . . . , z^(N)(k+K₁), wherein K₁ is a positiveinteger, are inputted to the blind mode equalizer system 2. Referring toFIG. 5, the signals 510 a, b, . . . , N are inputted to the bank ofestimation units 95 a, b, . . . N_(c) respectively, of the blind modeequalizer 2. The estimation units 95 a, b, . . . N_(c) have the sameblock diagrams as that of the estimation unit 95 in FIG. 1 except forthe added superscripts i in various expressions w_(jf) ^(i)(k), s_(j)^(i)(k), etc., to designate the estimation unit number i=1, 2, . . . ,N_(c) of FIG. 5 and N in the unit 95 of FIG. 1 is replaced by N_(a) inthe estimation units of FIG. 5.

Referring to FIG. 5, the estimation unit 95 i generates the filteredsignals 520 i(1, 2, . . . , N_(a)) s₁ ^(i), s₂ ^(i), . . . , s_(N) _(a)^(i) wherein N_(a) is the number of adaptive algorithms in theestimation unit 95 i. In some embodiments of the invention, the numberof adaptive algorithms in the various estimation units may be different.Referring to FIG. 5, the N=N_(c)N_(a) filtered signals s₁ ¹, s₂ ¹, . . ., s_(N) _(a) ¹, . . . , s₁ ^(N) ^(c) , s₂ ^(N) ^(c) , . . . , S_(N) _(a)^(N) ^(c) are inputted to the collator 550 that collates the N filteredsignals and makes the collated filtered signals 540 a though N s₁(k), .. . , s_(N)(k) available to the normalizing gain estimator block 90.

Referring to FIG. 5, the estimation unit 95 i makes available the N_(a)equalizer feed forward weight vectors w_(1f) ^(i), w_(2f) ^(i), . . . ,w_(N) _(a) _(f) ^(i) for i=1, 2, . . . , N_(c) to the collator 555. Thecollator 555 collates the N equalizer feed forward weight vectors andprovides the collated equalizer feed forward weight vectors 535 athrough N w_(1f)(k), . . . , w_(Nf)(k) to the normalizing gain estimatorblock 90. FIG. 2 shows the block diagram of the normalizing gainestimator that provides the N parameter α estimates α₁, . . . , α_(N) tothe DSP unit 60.

Referring to FIG. 5, the collated filtered signals 540 a though N s₁(k),. . . , s_(N)(k) are made available to the DSP unit. On the basis of theN filtered signals s₁(k), . . . , s_(N)(k), the DSP unit makes a jointestimate of the data symbol â(k). Referring to FIG. 5, the jointestimate of the data symbol h(k) is fed back to the bank of theestimation units 95 for providing the error signals for the update ofthe N adaptive algorithms.

Referring to FIG. 5, the joint estimate of the data symbol 565 â(k) isinputted to the feedback shift register 70 of length K₂ for some integerK₂. The feedback shift register makes available the K₂ delayed versions75 â(k−1), . . . , â(k−K₂) of the joint estimate of the data symbol 565â(k) to the scalar to vector converter 76. The scalar to vectorconverter 76 provides the equalizer feedback state vectorx_(b)(k)=[â(k−1) â(k−2) . . . â(k−K₂)]^(T) to the bank of the estimationunits 95 for cancelling the inter symbol interference due to the past K₂symbols. In various alternative embodiments of the invention, none ofthe N equalizer adaptive algorithms may be of the decision feedback typeand thus K₂ is zero.

In various embodiments of the invention, the number and type of theadaptive algorithms in the various estimation units 95 may be differentor use the same algorithm type but with different algorithm parameterssuch as the initial values of the equalizer weight vectors. In oneexample of the various embodiments, the number of diversity channelsN_(c) may be 3 with N_(a) equal to 1 for all three estimation units 95.The three estimation units in the example case may use the Goddard'salgorithm, the Sato's algorithm and the RLS algorithm respectively.

Various modifications and other embodiments of the invention applicableto various problems in Engineering and other fields will be readilyapparent to those skilled in the art in the field of invention. Themultiple algorithm architectures of the invention can be readilymodified and applied to various fields where such an architecture isapplicable. Examples of such fields in addition to various communicationsystems include Radars, sonar, digital audio systems, seismology,astronomy, and so on.

It is to be understood that the figures and descriptions of the presentinvention have been simplified to illustrate elements that are relevantfor a clear understanding of the present invention, while eliminatingother elements, for purposes of clarity. Those of ordinary skill in theart will recognize that these and other elements may be desirable.However, because such elements are well known in the art and becausethey do not facilitate a better understanding of the present invention,a discussion of such elements is not provided herein.

In general, it will be apparent to one of ordinary skill in the art thatat least some of the embodiments described herein, including, forexample, all of the modules of FIG. 1, may be implemented in manydifferent embodiments of software, firmware, and/or hardware, forexample, based on Field Programmable Gate Array (FPGA) chips orimplemented in Application Specific Integrated Circuits (ASICS). Thesoftware and firmware code may be executed by a computer or computingdevice comprising a processor (e.g., a DSP or any other similarprocessing circuit) including, for example, the computing device 600described below. The processor may be in communication with memory oranother computer readable medium comprising the software code. Thesoftware code or specialized control hardware that may be used toimplement embodiments is not limiting. For example, embodimentsdescribed herein may be implemented in computer software using anysuitable computer software language type, using, for example,conventional or object-oriented techniques. Such software may be storedon any type of suitable computer-readable medium or media, such as, forexample, a magnetic or optical storage medium. According to variousembodiments, the software may be firmware stored at an EEPROM and/orother non-volatile memory associated a DSP or other similar processingcircuit. The operation and behavior of the embodiments may be describedwithout specific reference to specific software code or specializedhardware components. The absence of such specific references isfeasible, because it is clearly understood that artisans of ordinaryskill would be able to design software and control hardware to implementthe embodiments based on the present description with no more thanreasonable effort and without undue experimentation.

FIG. 6 shows an example of a computing device 600 according to oneembodiment. For the sake of clarity, the computing device 600 isillustrated and described here in the context of a single computingdevice. However, it is to be appreciated and understood that any numberof suitably configured computing devices can be used to implement adescribed embodiment.

For example, in at least some implementations, multiple communicativelylinked computing devices may be used. One or more of these devices canbe communicatively linked in any suitable way such as via one or morenetworks. One or more networks can include, without limitation: theInternet, one or more local area networks (LANs), one or more wide areanetworks (WANs) or any combination thereof.

In the example of FIG. 6, the computing device 600 comprises one or moreprocessor circuits or processing units 602, one or more memory circuitsand/or storage circuit component(s) 604 and one or more input/output(I/O) circuit devices 606. Additionally, the computing device 600comprises a bus 608 that allows the various circuit components anddevices to communicate with one another. The bus 608 represents one ormore of any of several types of bus structures, including a memory busor memory controller, a peripheral bus, an accelerated graphics port,and a processor or local bus using any of a variety of busarchitectures. The bus 608 may comprise wired and/or wireless buses.

The processing unit 602 may be responsible for executing varioussoftware programs such as system programs, applications programs, and/orprogram modules/blocks to provide computing and processing operationsfor the computing device 600. The processing unit 602 may be responsiblefor performing various voice and data communications operations for thecomputing device 600 such as transmitting and receiving voice and datainformation over one or more wired or wireless communications channels.Although the processing unit 602 of the computing device 600 is shown inthe context of a single processor architecture, it may be appreciatedthat the computing device 600 may use any suitable processorarchitecture and/or any suitable number of processors in accordance withthe described embodiments. In one embodiment, the processing unit 602may be implemented using a single integrated processor.

The processing unit 602 may be implemented as a host central processingunit (CPU) using any suitable processor circuit or logic device(circuit), such as a as a general purpose processor. The processing unit602 also may be implemented as a chip multiprocessor (CMP), dedicatedprocessor, embedded processor, media processor, input/output (I/O)processor, co-processor, microprocessor, controller, microcontroller,application specific integrated circuit (ASIC), field programmable gatearray (FPGA), programmable logic device (PLD), or other processingdevice in accordance with the described embodiments.

As shown, the processing unit 602 may be coupled to the memory and/orstorage component(s) 604 through the bus 608. The bus 608 may compriseany suitable interface and/or bus architecture for allowing theprocessing unit 602 to access the memory and/or storage component(s)604. Although the memory and/or storage component(s) 604 may be shown asbeing separate from the processing unit 602 for purposes ofillustration, it is worthy to note that in various embodiments someportion or the entire memory and/or storage component(s) 604 may beincluded on the same integrated circuit as the processing unit 602.Alternatively, some portion or the entire memory and/or storagecomponent(s) 604 may be disposed on an integrated circuit or othermedium (e.g., hard disk drive) external to the integrated circuit of theprocessing unit 602. In various embodiments, the computing device 600may comprise an expansion slot to support a multimedia and/or memorycard, for example.

The memory and/or storage component(s) 604 represent one or morecomputer-readable media. The memory and/or storage component(s) 604 maybe implemented using any computer-readable media capable of storing datasuch as volatile or non-volatile memory, removable or non-removablememory, erasable or non-erasable memory, writeable or re-writeablememory, and so forth. The memory and/or storage component(s) 604 maycomprise volatile media (e.g., random access memory (RAM)) and/ornonvolatile media (e.g., read only memory (ROM), Flash memory, opticaldisks, magnetic disks and the like). The memory and/or storagecomponent(s) 604 may comprise fixed media (e.g., RAM, ROM, a fixed harddrive, etc.) as well as removable media (e.g., a Flash memory drive, aremovable hard drive, an optical disk).

Examples of computer-readable storage media may include, withoutlimitation, RAM, dynamic RAM (DRAM), Double-Data-Rate DRAM (DDRAM),synchronous DRAM (SDRAM), static RAM (SRAM), read-only memory (ROM),programmable ROM (PROM), erasable programmable ROM (EPROM), electricallyerasable programmable ROM (EEPROM), flash memory (e.g., NOR or NANDflash memory), content addressable memory (CAM), polymer memory (e.g.,ferroelectric polymer memory), phase-change memory, ovonic memory,ferroelectric memory, silicon-oxide-nitride-oxide-silicon (SONOS)memory, magnetic or optical cards, or any other type of media suitablefor storing information.

The one or more I/O devices 606 allow a user to enter commands andinformation to the computing device 600, and also allow information tobe presented to the user and/or other components or devices. Examples ofinput devices include data ports, analog to digital converters (ADCs),digital to analog converters (DACs), a keyboard, a cursor control device(e.g., a mouse), a microphone, a scanner and the like. Examples ofoutput devices include data ports, ADC's, DAC's, a display device (e.g.,a monitor or projector, speakers, a printer, a network card). Thecomputing device 600 may comprise an alphanumeric keypad coupled to theprocessing unit 602. The keypad may comprise, for example, a QWERTY keylayout and an integrated number dial pad. The computing device 600 maycomprise a display coupled to the processing unit 602. The display maycomprise any suitable visual interface for displaying content to a userof the computing device 600. In one embodiment, for example, the displaymay be implemented by a liquid crystal display (LCD) such as atouch-sensitive color (e.g., 76-bit color) thin-film transistor (TFT)LCD screen. The touch-sensitive LCD may be used with a stylus and/or ahandwriting recognizer program.

The processing unit 602 may be arranged to provide processing orcomputing resources to the computing device 600. For example, theprocessing unit 602 may be responsible for executing various softwareprograms including system programs such as operating system (OS) andapplication programs. System programs generally may assist in therunning of the computing device 600 and may be directly responsible forcontrolling, integrating, and managing the individual hardwarecomponents of the computer system. The OS may be implemented, forexample, as a Microsoft® Windows OS, Symbian OS™, Embedix OS, Linux OS,Binary Run-time Environment for Wireless (BREW) OS, JavaOS, or othersuitable OS in accordance with the described embodiments. The computingdevice 600 may comprise other system programs such as device drivers,programming tools, utility programs, software libraries, applicationprogramming interfaces (APIs), and so forth.

In various embodiments disclosed herein, a single component may bereplaced by multiple components and multiple components may be replacedby a single component to perform a given function or functions. Exceptwhere such substitution would not be operative, such substitution iswithin the intended scope of the embodiments.

While various embodiments have been described herein, it should beapparent that various modifications, alterations, and adaptations tothose embodiments may occur to persons skilled in the art withattainment of at least some of the advantages. The disclosed embodimentsare therefore intended to include all such modifications, alterations,and adaptations without departing from the scope of the embodiments asset forth herein.

Embodiments may be provided as a computer program product including anon-transitory machine-readable storage medium having stored thereoninstructions (in compressed or uncompressed form) that may be used toprogram a computer (or other electronic device) to perform processes ormethods described herein. The machine-readable storage medium mayinclude, but is not limited to, hard drives, floppy diskettes, opticaldisks, CD-ROMs, DVDs, read-only memories (ROMs), random access memories(RAMs), EPROMs, EEPROMs, flash memory, magnetic or optical cards,solid-state memory devices, or other types of media/machine-readablemedium suitable for storing electronic instructions. Further,embodiments may also be provided as a computer program product includinga transitory machine-readable signal (in compressed or uncompressedform). Examples of machine-readable signals, whether modulated using acarrier or not include, but are not limited to, signals that a computersystem or machine hosting or running a computer program can beconfigured to access, including signals downloaded through the Internetor other networks. For example, the distribution of software may be anInternet download.

1. A blind mode multiple algorithms equalizer system (BMMAES) to recoverthe in general complex valued data symbols from a signal transmittedover a time-varying dispersive diversity wireless channel with an orderof diversity N_(c), the system comprised of: a bank of N_(c) estimationsunits wherein the estimation unit is comprised of a feed forward shiftregister for providing a feed forward state vector to a firstmultiplicity N_(a) inner product operators; a multiplicity N_(a)distinct adaptive algorithms with N_(a) in the range of 1 and an integerN_(a,max) for providing the N_(a) equalizer forward weight vectors tothe first multiplicity N_(a) inner product operators for providing theN_(a) feed forward signals comprising the first components of the N_(a)filtered estimates of the data symbols wherein the type and themultiplicity N_(a) of the adaptive algorithms may be different in theN_(c) estimation units; a collator for collating the filtered estimatesof the data symbols from the aggregate number N of the adaptivealgorithms providing the collated N filtered estimates of the datasymbols wherein N is in the range of N_(c) and the productN_(c)N_(a,max); and a DSP unit for providing the jointly detected datasymbol based on the collated N filtered estimates of the data symbols.2. The system of claim 1, wherein the blind mode multiple algorithmsequalizer system further comprises a feedback shift register forproviding a feedback state vector to a second multiplicity N_(a) innerproduct operators of the estimation unit for providing the N_(a)feedback signals comprising second components of the N_(a) filteredestimates of the data symbols.
 3. The system of claim 1 wherein amultiplicity N_(a) adaptive algorithms are for further providing theN_(a) equalizer feedback weight vectors to the second multiplicity N_(a)inner product operators of the estimation unit.
 4. The system of claim 2wherein the second components of the Na filtered estimates of the datasymbols are set equal to
 0. 5. The system of claim 1 wherein the blindmode multiple algorithms equalizer system further comprised of anormalizing gain estimator for providing the multiplicity N parameter αestimates to the DSP unit for normalizing the signal power in thecollated N filtered estimates of the data symbols.
 6. The system ofclaim 1 wherein the DSP unit is further comprised of: phase alignmentsubsystems 1 through N for providing gain normalization and phasealignment of the collated N filtered signals; a reference phasegenerator for generating the reference phase; a means of furtheradjusting the phase of the filtered signals; a combiner weightsgenerator; a weighted combiner for weighted combining of the phaseadjusted signals; a decision device for providing the jointly detecteddata symbol.
 7. The system of claim 6 wherein phase alignment subsystemi for i equal to 1 through N is further comprised of: a gain normalizer;a phase accumulator unit; a decision device for providing the i^(th)detected data symbol; a phase threshold device for providing thedetected phase φ_(i); a means for estimating the signal to residualinter symbol interference (ISI) plus noise power ratio Γ_(i).
 8. Thesystem of claim 1 wherein complex valued data symbols are the modulatedsignals modulated according to at least one method selected from thegroup consisting of the M-quadrature amplitude modulation (MQAM),M-phase shift keying (MPSK), and M-pulse amplitude modulation (MPAM)modulated signals, wherein the order of modulation M is the number ofpoints in the signal constellation.
 9. The system of claim 7 wherein thedetected phase φ_(i) corresponds to the sector of the rotationalsymmetry of the signal constellation of the data symbols containing thei^(th) gain normalized and phase aligned filtered signal.
 10. The systemof claim 6 wherein the combiner weights are based on the N signal toresidual inter symbol interference (ISI) plus noise power ratiosaccording to the maximal ratio diversity combining technique.
 11. Thesystem of claim 6 wherein the reference phase generator is for furtherpartitioning the phase adjusted filtered signals 1 through N accordingto the corresponding detected N phase φ₁ through φ_(N) and for providingthe set S_(p) containing the maximum number of the phase adjustedfiltered signals.
 12. The system of claim 6 wherein the combiner weightsfor the signals in the set S_(p) are based on the signal to ISI plusnoise power ratios for the set of signals S_(p) with the combinerweights for the signals not belonging to the set S_(p) set equal to 0.13. The system of claim 6 wherein the combiner weights are determinedaccording to Sato's algorithm
 14. The system of claim 6 wherein thecombiner weight for the signal in the set S_(p) with the maximum signalto ISI plus noise power ratio is set equal to 1 with all other weightsset equal to
 0. 15. The system of claim 1 wherein both N_(c) and theaggregate number N of the adaptive algorithms are equal to 3 and whereinthe N adaptive algorithms are all distinct.
 16. The system of claim 1wherein the distinct adaptive algorithms are selected from the groupconsisting of the recursive least squares (RLS) algorithm, quantizedstate algorithm (QS), LMS algorithm, Sato's algorithm, and the constantmodulus (CMA) algorithm.
 17. A computer-implemented method forrecovering the complex valued data symbols from the signals transmittedover time-varying dispersive diversity wireless channel with order ofdiversity N_(c), the method comprising: receiving, by a computer device,the channel output signal, wherein the computer device comprises atleast one memory and associated memory device; implementing, by thecomputer device, a bank of N_(c) estimations units wherein theestimation unit is comprised of a feed forward shift register forproviding a feed forward state vector to a first multiplicity N_(a)inner product operators; a multiplicity N_(a) distinct adaptivealgorithms with N_(a) in the range of 1 and an integer N_(a,max) forproviding the N_(a) equalizer forward weight vectors to the firstmultiplicity N_(a) inner product operators for providing the N_(a) feedforward signals comprising the first components of the N_(a) filteredestimates of the data symbols wherein the type and the multiplicityN_(a) of the adaptive algorithms are different in the N_(a) estimationunits; implementing, by the computer device, a collator for collatingthe filtered estimates of the data symbols from the aggregate number Nof the adaptive algorithms providing the collated N filtered estimatesof the data symbols wherein N is in the range of N_(c) and the productN_(c)N_(a,max); and implementing, by the computer device, a DSP unit forproviding the jointly detected data symbol based on the collated Nfiltered estimates of the data symbols.
 18. The method of claim 17,wherein the method is further comprised of implementing, by the computerdevice, a feedback shift register for providing a feedback state vectorto a second multiplicity N_(a) inner product operators of the estimationunit for providing the N_(a) feedback signals comprising the secondcomponents of the N_(a) filtered estimates of the data symbols.
 19. Themethod of claim 17 wherein a multiplicity N_(a) possibly distinctadaptive algorithms are for further providing the N_(a) equalizerfeedback weight vectors to the second multiplicity N_(a) inner productoperators of the estimation unit.
 20. The method of claim 18 wherein thesecond components of the N_(a) filtered estimates of the data symbolsare set equal to
 0. 21. The method of claim 17 wherein the DSP unit isfurther comprised of: phase alignment subsystems 1 through N forproviding gain normalization and phase alignment of the collated Nfiltered signals; a reference phase generator for generating thereference phase; a means of further adjusting the phase of the filteredsignals; a combiner weights generator; a weighted combiner for weightedcombining of the phase adjusted signals; a decision device for providingthe jointly detected data symbol.
 22. The method of claim 21 whereinphase alignment subsystem i for i equal to 1 through N is furthercomprised of: a gain normalizer; a phase accumulator unit; a decisiondevice for providing the i^(th) detected data symbol; a phase thresholddevice for providing the detected phase φ_(i); a means for estimatingthe signal to residual inter symbol interference (ISI) plus noise powerratio Γ_(i); and the combiner weights are based on the signal toresidual ISI plus noise power ratios.